What is zoning?
Your zone is the area you control with your champion. Zoning means controlling your enemy's location and pushing them away from minions by making them afraid of entering your zone. This is beneficial because they will not be able to last hit minions, so they will have less gold to buy items later. Additionally, by pushing enemy champions far back enough, you can even deny them experience from dying minions. Achieving this can be extremely advantageous, as your opponents can end up both undergeared and underlevelled.
How can I zone?
There are several ways to scare opponents away from your zone, including:
- Dealing more damage than they deal to you.
- Hiding in the bushes and making them fear a gank (either from a jungler or from a fellow laner that travels quickly).
Some tactics are more effective than others. For instance, if your enemy laner knows that you can kill them if you get within range, your zone is limited to the range of your attacks and abilities. But if you are hiding in the bushes, your zone covers virtually the entire lane, as your enemies don't know what bush you are in.
Certain champions are better at zoning than others, and certain combinations can be very effective. Ranged champions typically have an advantage, but melee champions can also be good zoners. For example, 
Xin Zhao is an excellent zoner. His 
Audacious Charge has a moderate range and it slows, preventing enemy escape for a few seconds. His 
Three Talon Strike makes it even more difficult to escape him with its Knock-Up. Combining this with good damage output and a fellow laner can quickly take out an enemy. All of this makes Xin a very proficient zoner. Coupling him with a 
Lux with proper coordination can almost assure a kill.
You can also zone by gradually pushing an enemy towards one side of the lane. This can be useful when setting up a gank. For example, junglers will typically try to gank in the bottom lane by hiding in the bush near the river waiting for the right moment to strike. To increase the chances of a successful gank, the bottom laner can stay in the outer edge of the lane to force the enemy laner to go to the inside, near the river bush. This makes it much easier for the jungler to jump on the enemy.
Strong zoners
Crowd control and high damage output are the main traits of strong zoners. For melee champions a gap closer can also be very beneficial. The enemy's sustainability in the lane can be used to counter virtually any harass and allied sustain can be useful to leave the enemy zoned for longer as the enemy will probably have to poke back to regain position in lane. Some potentially strong zoners:
Akali becomes an excellent zoner at level 6. She gains a huge gap-closer with her ultimate, which can be very intimidating to a squishy target and may even scare them out of the lane.- Annie is an excellent zoner in a solo lane, thanks to her passive Pyromania and her farming sustain with Disintegrate. When farming she can control a lane by activating her stun. Coupling it with her bursting, she can prevent enemy champions from coming into her range, giving her a good lane dominance.
- Anivia has one of the highest autoattack ranges in the game, allowing her to hit her enemies from afar without fear of retaliation.
- Blitzcrank is an excellent zoner in a duo lane, especially when paired with a heavy damage-dealer. His zoning relies on Rocket Grab, as frightening as it can be it can be blocked by minions.
- Caitlyn is an excellent zoner in any lane. Her main zoning technique is laying Yordle Snap Traps, discouraging the enemy from utilizing brush/limiting their movement. If they do step on one, you can repeatedly autoattack for significant damage. If you charge up Headshot the threat of the nuke will push most champions back. Piltover Peacemaker does massive amounts of damage if it hits.
- Cassiopeia is a very powerful zoner in any lane. Her Noxious Blast is enormously strong for harassment. Also, if either Noxious Blast or Miasma hit, her zoning capability becomes more powerful due to her spammable Twin Fang.
- Heimerdinger's H-28G Evolution Turret are useful for zoning and Hextech Micro-Rockets are useful for poking. The abilities combined can easily force a champion to retreat under their tower.
- Irelia's Bladesurge is not only a good ability with which to last hit minions, but it can also be used as a gap closer to reach enemy champions. Using Equilibrium Strike and a few autoattacks afterward can deal a fair amount of damage will little fear of retaliation as Irelia can simply Bladesurge to another minion if the ability isn't on cooldown.
- Jax is a very effective zoner with his Leap Strike + Empower combo.
- Karthus is a great zoner. His zoning capability is great when duo laning, but is best in a solo lane, where he can spam his Lay Waste on the opposing champion and deal double damage if the enemy is alone.
- LeBlanc is an extremely effective zoner in any lane. Her Sigil of Malice combined with another spell can put out incredible damage. The slow/snare from Ethereal Chains can prevent enemies from escaping on top of providing even more damage. When she acquires Distortion and Mimic, her zoning potential increases even more.
- Lux zones well with fairly high burst damage, and strong CC abilities. The snare from Light Binding is her primary advantage in zoning, as the CC prevents enemies from escaping as she casts Lucent Singularity and procs Illumination with autoattacks.
- Renekton's Slice / Dice allows him to cover a fair amount of distance in a short amount of time. Following Slice / Dice with Cull the Meek and Ruthless Predator can deal a significant amount of burst damage early in the game. Although the cooldown on Slice / Dice is fairly long, it is spammable because Renekton is manaless.
- Ryze's Overload is on a very short cooldown and can be available practically any time an enemy champion would want to last hit. This can be especially effective against a melee champion.
- Singed gives him a great deal of zoning potential. His Mega Adhesive makes it difficult to get away if it is placed well, and his Poison Trail can put out steady damage at its higher levels.
- Taric has a moderate range and is one of the best stuns in the game, and his heal can keep him and his teammate alive for quite a long time. By himself, his zoning ability isn't so great. But when put with a champion with high early game damage, he can be very good at it.
- Tristana's range allows her to poke champions. Her Explosive Shot passive makes her a strong pusher, while the active can shut down champs like Warwick or Dr. Mundo and thanks to her Rocket Jump and Buster Shot it is hard to gank her.
- Urgot is one of the best zoners in the game. He shines best in a 1v1 lane, where he can abuse the massive range on his locked-on Acid Hunter following a Noxian Corrosive Charge. The enormous range of this combo essentially guarantees that he will be able to use the entire combo while being relatively safe from retaliation.
- Xin Zhao: As explained above, his damage combined with his CC makes him an excellent laner, as his charge outranges a lot of champion skills and almost all auto-attacks.
